where \({\mathbb {1}}_{(\cdot )}\)  is the indicator function, and \(g_-, g_M, g_+\)  are suitable polynomials.
To ensure high accuracy in the approximation, \(g_M\)  is defined as a Lagrange polynomial of high-degree \(M-1\) . The CPs \(\xi \) , which identify the Lagrange basis in (REF ), are chosen as Chebyshev nodes in the bounded interval \(\Omega _M=[-\bar{\xi }, \bar{\xi }]\)  [1]}. Instead, the CVs \(\mathbf {a}\)  are defined as in (REF ).
The choice of Chebyshev nodes allows to increase the degree of the interpolation (i.e. the number of CPs and CVs), avoiding the Runge's phenomenon within the interval \(\Omega _M\)  [2]}. However, the behaviour of \(g_M\)  outside \(\Omega _M\)  is out of control. We expect the high-degree polynomial \(g_M\)  to be a poor approximation of \(g\)  in \(\Omega _-\)  and \(\Omega _+\) . Therefore, we define \(g_-\)  and \(g_+\)  as linear (or at most quadratic) polynomials, with degree \(M_--1\)  and \(M_+-1\) , built on the extreme CPs of \(\xi \) .
